Vector Optimization with Infimum and Supremum [electronic resource] /
Löhne, Andreas.author.
The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.
Description based upon print version of record.
Includes bibliographical references and index.
pt. 1. General and convex problems -- pt. 2. Linear problems.
The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.
Operations research.
Decision making.
Mathematical optimization.
Algebra.
Ordered algebraic structures.
Management science.
Algorithms.
Operations Research/Decision Theory.
Optimization.
Order, Lattices, Ordered Algebraic Structures.
Operations Research, Management Science.
Algorithms.